Home > Calculus > Determining Limits Algebraically

How do you find the Limit of #ln(lnx) / x# as x approaches infinity?

Answer 1

Ezekiel Alexander

Using L'Hôpital's rule #lim_(x->oo)ln(ln(x))/x=lim_(x->oo)(1/lnx1/x)/1=0#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Samantha Adkison

To find the limit of ln(lnx) / x as x approaches infinity, we can use L'Hôpital's rule. Taking the derivative of both the numerator and denominator separately, we get (1/lnx) / 1. As x approaches infinity, the natural logarithm of x also approaches infinity. Therefore, the limit becomes 1/∞, which equals 0. Hence, the limit of ln(lnx) / x as x approaches infinity is 0.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.